2020 CIME I Problems/Problem 7

Problem 7

For every positive integer $n$ , define $f(n)=\frac{n}{1 \cdot 3 \cdot 5 \cdots (2n+1)}.$ Suppose that the sum $f(1)+f(2)+\cdots+f(2020)$ can be expressed as $\frac{p}{q}$ for relatively prime integers $p$ and $q$ . Find the remainder when $p$ is divided by $1000$ .

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2020 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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2020 CIME I Problems/Problem 7

Problem 7

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